Symbolic Software for the Painlevé Test of Nonlinear Ordinary and Partial Differential Equations

DOI10.2991/jnmp.2006.13.1.8zbMath1110.35300arXivnlin/0505004OpenAlexW3105563462MaRDI QIDQ3432946

Douglas E. Baldwin, Willy Hereman

Publication date: 19 April 2007

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0505004

zbMATH Keywords

KdV equationsHirota-Satsuma equationalgorithm for Painlevé testreview of symbolic algorithms

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Software, source code, etc. for problems pertaining to partial differential equations (35-04)

Related Items (17)

Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter ⋮ Painlevé analysis for a new integrable equation combining the modified Calogero-Bogoyavlenskii-Schiff (MCBS) equation with its negative-order form ⋮ A note on the Painlevé test for nonlinear variable-coefficient PDEs ⋮ A study of the symmetry analysis for the Hirota-Satsuma equations ⋮ A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions ⋮ Construction of exact partial solutions of nonintegrable systems by means of formal Laurent and Puiseux series ⋮ Painlevé test, complete symmetry classifications and exact solutions to R-D types of equations ⋮ Understanding complex dynamics by means of an associated Riemann surface ⋮ Integrability characteristics of a novel (2+1)-dimensional nonlinear model: Painlevé analysis, soliton solutions, Bäcklund transformation, Lax pair and infinitely many conservation laws ⋮ A symbolic algorithm for computing recursion operators of nonlinear partial differential equations ⋮ A modified WTC algorithm for the Painlevé test of nonlinear variable-coefficient PDEs ⋮ Diversity of interaction solutions of a shallow water wave equation ⋮ Negative-order integrable modified KdV equations of higher orders ⋮ Applicable symbolic computations on dynamics of small-amplitude long waves and Davey-Stewartson equations in finite water depth ⋮ Painlevé analysis of a nonlinear Schrödinger equation discussing dynamics of solitons in optical fiber ⋮ Painlevé analysis for various nonlinear Schrödinger dynamical equations ⋮ Multiple-soliton solutions and lumps of a \((3+1)\)-dimensional generalized KP equation

Uses Software

• Mathematica
• PainleveTest

Cites Work

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• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• A unified approach to Painlevé expansions
• Self-intersection of the complex separatrices and the nonexistence of the integrals in the Hamiltonian systems with one-and-half degrees of freedom
• A perturbative Painlevé approach to nonlinear differential equations
• Implementation of the Painlevé test for ordinary differential systems
• PDEPtest: a package for the Painlevé test of nonlinear partial differential equations
• A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
• Lie transformations, nonlinear evolution equations, and Painlevé forms
• The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
• Derivation and implicit solution of the Harry Dym equation and its connections with the Korteweg-de Vries equation
• The Painlevé property for partial differential equations
• The Connection between Partial Differential Equations Soluble by Inverse Scattering and Ordinary Differential Equations of Painlevé Type
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. II
• A new hierarchy of Korteweg–de Vries equations
• The singular manifold method revisited
• Integrals of nonlinear equations of evolution and solitary waves
• Necessary condition for the existence of algebraic first integrals

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